Trigonometry Examples

(2 x + 5) (2 x - 5)

$(2 x + 5) (2 x - 5)$

Step 1

Expand

(2 x + 5) (2 x - 5)

$(2 x + 5) (2 x - 5)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

2 x (2 x - 5) + 5 (2 x - 5)

$2 x (2 x - 5) + 5 (2 x - 5)$

Step 1.2

Apply the distributive property.

2 x (2 x) + 2 x \cdot - 5 + 5 (2 x - 5)

$2 x (2 x) + 2 x \cdot - 5 + 5 (2 x - 5)$

Step 1.3

Apply the distributive property.

2 x (2 x) + 2 x \cdot - 5 + 5 (2 x) + 5 \cdot - 5

$2 x (2 x) + 2 x \cdot - 5 + 5 (2 x) + 5 \cdot - 5$

2 x (2 x) + 2 x \cdot - 5 + 5 (2 x) + 5 \cdot - 5

$2 x (2 x) + 2 x \cdot - 5 + 5 (2 x) + 5 \cdot - 5$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

2 \cdot 2 x \cdot x + 2 x \cdot - 5 + 5 (2 x) + 5 \cdot - 5

$2 \cdot 2 x \cdot x + 2 x \cdot - 5 + 5 (2 x) + 5 \cdot - 5$

Step 2.1.2

Multiply

x

$x$ by

x

$x$ by adding the exponents.

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Step 2.1.2.1

Move

x

$x$ .

2 \cdot 2 (x \cdot x) + 2 x \cdot - 5 + 5 (2 x) + 5 \cdot - 5

$2 \cdot 2 (x \cdot x) + 2 x \cdot - 5 + 5 (2 x) + 5 \cdot - 5$

Step 2.1.2.2

Multiply

x

$x$ by

x

$x$ .

2 \cdot 2 x^{2} + 2 x \cdot - 5 + 5 (2 x) + 5 \cdot - 5

$2 \cdot 2 x^{2} + 2 x \cdot - 5 + 5 (2 x) + 5 \cdot - 5$

2 \cdot 2 x^{2} + 2 x \cdot - 5 + 5 (2 x) + 5 \cdot - 5

$2 \cdot 2 x^{2} + 2 x \cdot - 5 + 5 (2 x) + 5 \cdot - 5$

Step 2.1.3

Multiply

2

$2$ by

2

$2$ .

4 x^{2} + 2 x \cdot - 5 + 5 (2 x) + 5 \cdot - 5

$4 x^{2} + 2 x \cdot - 5 + 5 (2 x) + 5 \cdot - 5$

Step 2.1.4

Multiply

- 5

$- 5$ by

2

$2$ .

4 x^{2} - 10 x + 5 (2 x) + 5 \cdot - 5

$4 x^{2} - 10 x + 5 (2 x) + 5 \cdot - 5$

Step 2.1.5

Multiply

2

$2$ by

5

$5$ .

4 x^{2} - 10 x + 10 x + 5 \cdot - 5

$4 x^{2} - 10 x + 10 x + 5 \cdot - 5$

Step 2.1.6

Multiply

5

$5$ by

- 5

$- 5$ .

4 x^{2} - 10 x + 10 x - 25

$4 x^{2} - 10 x + 10 x - 25$

4 x^{2} - 10 x + 10 x - 25

$4 x^{2} - 10 x + 10 x - 25$

Step 2.2

Add

- 10 x

$- 10 x$ and

10 x

$10 x$ .

4 x^{2} + 0 - 25

$4 x^{2} + 0 - 25$

Step 2.3

Add

4 x^{2}

$4 x^{2}$ and

0

$0$ .

4 x^{2} - 25

$4 x^{2} - 25$

4 x^{2} - 25

$4 x^{2} - 25$